2. Three masses are constrained to move horizontally in one dimension with no friction. Mass 1 has mass, M, and initial velocity, vo, towards mass 2. Mass 1 collides with mass 2 at time f = 0. Mass 2 and 3 have identical mass, m, and are connected by an ideal spring of negligible mass spring constant k. Masses 2 and 3 are initially at rest and the spring is initially at its equilibrium length. Assume all collisions are elastic and of very short duration and that the spring is long enough that it never becomes fully compressed. k (A) What is the natural frequency of oscillation, @, for M m m the two coupled masses? (B) Immediately after the collision, what are the velocities of each of the three masses, v, (0), v2(0), v,(0)? (C) In terms of v, (0), v2(0), and v;(0), write down the positions of each mass, x,(1), x2(1) and x, (1), relative to their positions at f = 0, for all f > 0, assuming there are no additional collisions. (D) What is the minimum mass, M, so that mass 1 will collide with mass 2 a second time